From experience and asking neighbours in my area (and on here last year) - stocking density for my land varies from 2-6 an acre without supplimentary feeding, down to these variables;
Rotational grazing or not;
Feeding on the land or not;
Fertilizing of the land;
Breed of sheep.
To give an idea, If you graze down to 4cm, however long it takes, then move paddocks... you will get the best grass growth, but you could do set timeings which has the benefit of creating long grass areas, more wildlife and less worm/parasite burden (i currently practise this, but may experiment in time).
If you feed hay on the land a) you eek out the grass and b) the manure from the hay adds fertility so improving grass growth, so a double edged sword of greatness increasing your carrying cap.
Add nitroen in May and well - you can grow grass faster than 12 sheep an acre can eat it for 5 weeks or so.
Breed - 12 hebrideans eat about the same grass as 4 texels in my experience on my land, and the same as 5 NEM Mules, and 7-8 Lleyns......... they are smaller sheep though